The club had previously said it was was shutting Section 111, citing safety grounds such as "lateral movement" within the section, caused by the self-style ultras.
Other concerns related to overcrowding, the refusal of spectators to comply with stewards, mock fighting and body surfing of young people over the heads of spectators.
Last month, Uefa opened an investigation into the "setting off of fireworks" at the home European game against Irish club Cliftonville.
Celtic's decision comes just days before they face Shakter Karagandy in the home leg of a crucial Champions League qualifier, seeking to overturn a 2-0 reverse.
The Green Brigade have been credited in some quarters for helping engender a special atmosphere at Celtic Park.
The club's statement read: "Celtic Football Club announced today that it has suspended the relocation of Season Books for supporters within Section 111 at Celtic Park.
"Following extensive and positive discussions with supporters' representatives for the Section, the Club has received assurances relating to previously raised safety concerns and unsafe behaviour within the stadium.
"Celtic has engaged with the Glasgow City Council Safety Advisory Group regarding this matter and they have noted these assurances. This matter will be monitored on an ongoing, match -by-match, basis by both the Club and the Safety Advisory Group.
"Celtic Football Club would like to re-iterate its commitment and responsibility to ensuring the safety of everyone who visits Celtic Park. It is our absolute priority.
"The Club is pleased to have engaged in positive dialogue in relation to this matter. We thank the Safety Advisory Group and supporters' representatives for their continued co-operation and we look forward to working together to ensure a safe environment in the stadium."
The Green Brigade said in a statement: "The Green Brigade are pleased to announce that a positive outcome relating to Section 111 has been reached after constructive discussions with the Club. All relocations away from our block within Section 111 have now been reversed with all of those affected being returned to their original seat.
"As always we must thank the Celtic support who once again rallied around our Group and section when it was needed. We would like to especially thank all fans within our block for their patience and resilience over the past few weeks as we tried to reach a positive conclusion.
"We are now satisfied that this has been achieved and look forward to returning to Celtic Park on Saturday to resume normal practice. Furthermore we look forward to working together with the Club on a project to introduce a Safe Standing section to Celtic Park.
"Given relocations have already taken place - and the late nature in arriving at this conclusion - current/original season tickets will no longer be active.For Saturday's match paper tickets will be issued for all within the block and will be distributed before the match. Tickets will be available for collection from 1pm at the ticket office behind the Superstore and will only be issued after presenting your 111 teamcard. We understand that this may be problematic however will strive to make the process as smooth as possible."